Many problems in biophysics involve the interaction of an incompressible fluid and an
immersed elastic interface. The solution to these problems can be approximated using the
immersed boundary (IB) method, which was developed in [1]} to simulate
blood flow through the heart. The relative ease by which the IB method can be
incorporated into a Navier-Stokes solver has led to its popularity in myriad applications
(see, e.g. [2]}, [3]} and references therein). The IB method
couples the equations governing fluid velocity and pressure to those governing the
interface movement and elastic forces via operations we will refer to as
interpolation and spreading. Fluid velocities are interpolated to points on
the interface, and forces on the interface are spread to the fluid. Fluid properties are
discretized on a fixed Eulerian grid. The interface is represented by a set of mobile
Lagrangian points. This presents a problem for effective parallelization of interpolation
and spreading, as these operators must be reconstructed at each timestep to account for
the motion of the Lagrangian points relative to the Eulerian grid. The Eulerian and
Lagrangian points, on the other hand, can be treated as fixed in their respective
coordinate spaces for several timesteps, if not for the entirety of a simulation. We may
therefore treat solving the fluid equations and computing elastic forces as the result of
a black-box computation and focus primarily on the interpolation and spreading
operations.
